Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications
In this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. It can be asymmetric, such as bathtub, unimodal, incr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/3/587 |
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| author | Naif Alotaibi Ibrahim Elbatal Mansour Shrahili A. S. Al-Moisheer Mohammed Elgarhy Ehab M. Almetwally |
| author_facet | Naif Alotaibi Ibrahim Elbatal Mansour Shrahili A. S. Al-Moisheer Mohammed Elgarhy Ehab M. Almetwally |
| author_sort | Naif Alotaibi |
| collection | DOAJ |
| description | In this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. It can be asymmetric, such as bathtub, unimodal, increasing and decreasing. In addition, the shape forms of the hrf for the KMKu model can be bathtub, U-shaped, J-shaped and increasing. Several statistical and computational properties were computed. Four different measures of entropy were studied. The maximum likelihood approach was employed to estimate the parameters for the KMKu model under simple and ranked set sampling. A simulation experiment was conducted in order to calculate the model parameters of the KMKu model utilizing simple and ranked set sampling and show the efficiency of the ranked set sampling more than the simple random sampling. The KMKu has more flexibility than the Ku model and other well-known models, and we proved this using three real-world data sets. |
| first_indexed | 2024-03-11T05:50:46Z |
| format | Article |
| id | doaj.art-f98c551eb1d34856a4324d4a83a6feae |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T05:50:46Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f98c551eb1d34856a4324d4a83a6feae2023-11-17T14:08:06ZengMDPI AGSymmetry2073-89942023-02-0115358710.3390/sym15030587Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with ApplicationsNaif Alotaibi0Ibrahim Elbatal1Mansour Shrahili2A. S. Al-Moisheer3Mohammed Elgarhy4Ehab M. Almetwally5Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11432, Saudi ArabiaDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, Jouf University, P.O. Box 848, Sakaka 72351, Saudi ArabiaMathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, EgyptFaculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, EgyptIn this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. It can be asymmetric, such as bathtub, unimodal, increasing and decreasing. In addition, the shape forms of the hrf for the KMKu model can be bathtub, U-shaped, J-shaped and increasing. Several statistical and computational properties were computed. Four different measures of entropy were studied. The maximum likelihood approach was employed to estimate the parameters for the KMKu model under simple and ranked set sampling. A simulation experiment was conducted in order to calculate the model parameters of the KMKu model utilizing simple and ranked set sampling and show the efficiency of the ranked set sampling more than the simple random sampling. The KMKu has more flexibility than the Ku model and other well-known models, and we proved this using three real-world data sets.https://www.mdpi.com/2073-8994/15/3/587Kumaraswamy modelasymmetricranked set samplingKM transformation familysimulationmaximum likelihood estimation |
| spellingShingle | Naif Alotaibi Ibrahim Elbatal Mansour Shrahili A. S. Al-Moisheer Mohammed Elgarhy Ehab M. Almetwally Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications Symmetry Kumaraswamy model asymmetric ranked set sampling KM transformation family simulation maximum likelihood estimation |
| title | Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications |
| title_full | Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications |
| title_fullStr | Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications |
| title_full_unstemmed | Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications |
| title_short | Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications |
| title_sort | statistical inference for the kavya manoharan kumaraswamy model under ranked set sampling with applications |
| topic | Kumaraswamy model asymmetric ranked set sampling KM transformation family simulation maximum likelihood estimation |
| url | https://www.mdpi.com/2073-8994/15/3/587 |
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